An improved active disturbance rejection control implementation method and control system based on gain scheduling

Abstract

The present invention provides an improved active disturbance rejection control implementation method and control system based on gain scheduling, comprising the following steps: using a high-order inertial system to describe a class of actual industrial systems; selecting a controlled variable as a scheduling parameter and dividing the number of scheduling intervals; applying a compensation algorithm to a current controlled variable to obtain an output of a compensation algorithm; using the output of the compensation algorithm and the output of the actual industrial system as inputs of an extended state observer algorithm, and obtaining the output of the actual industrial system, multi-order derivatives of the actual industrial system, and an observed value of the total disturbance received by the extended state observer algorithm; using the observed value and a set value of the controlled variable of the actual industrial system as inputs, and obtaining a control variable to be adjusted through a control law algorithm; and adjusting parameters in the improved active disturbance rejection control algorithm in real time through a scheduling parameter switching method. The present invention can adjust the parameters of the improved active disturbance rejection control algorithm in real time according to the working conditions of the actual industrial system, thereby achieving a satisfactory control effect.

Description

Technical Field

[0001] The present invention relates to the field of industrial control, and in particular to an improved active disturbance rejection control implementation method and control system based on gain scheduling. Background Art

[0002] The ADRC algorithm has been widely used in robotic systems, power systems, and thermal systems due to its simple structure, good tracking and anti-interference performance, and strong robustness. However, in typical industrial process control such as chemical processes and thermal power generation processes, there are some processes with large lags, such as the denitrification system and main steam pressure system in thermal power generation, which are generally described by high-order inertial systems. Where s, K, T, and n represent the differential operator, the gain of the high-order inertial system, the time constant of the high-order inertial system, and the order of the high-order inertial system, respectively, and n ≥ 3. Y(s) and U(s) are the output and input of the high-order inertial system, respectively. Taking the denitrification system as an example, the meanings of the parameters in the above formula are: the output Y(s) is the output value of the nitrogen oxide concentration of the denitrification system, the input U(s) is the ammonia injection amount of the denitrification system, the gain coefficient K refers to the amplification factor of the input value by the high-order system, and the input value is the change in the nitrogen oxide concentration of the denitrification system corresponding to 1 ton of ammonia injection. The time constant T refers to the time required for the system response to reach 63.2% of the steady-state value.

[0003] For this type of high-order inertial system, there are standard active disturbance rejection control algorithms and improved active disturbance rejection control algorithms, which can improve the tracking performance and anti-interference performance of high-order inertial systems to a certain extent.

[0004] Specifically, the implementation process of the standard ADRC algorithm is as follows: Figure 1 As shown; as CN108287466B an improved auto-disturbance rejection control method for a class of high-order systems gives an improved auto-disturbance rejection control algorithm, the implementation process is as follows Figure 2 As shown in the figure, the standard active disturbance rejection control algorithm is used to control high-order inertial systems. When the anti-interference performance is strong, the tracking performance is poor, and when the tracking performance is strong, the anti-interference performance is poor. The existing improved automatic anti-disturbance control algorithm can well balance the tracking and anti-interference performance under the design working conditions. However, when the working conditions deviate from the design conditions, the control performance will be significantly reduced, making it impossible for the actual industrial system to maintain good control performance under all working conditions. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the existing technology. For a type of actual industrial system that can be described in series with an inertia link, an improved active disturbance rejection control implementation method and control system based on gain scheduling are provided. By selecting the controlled quantity as the scheduling parameter and the number of scheduling intervals, a gain scheduling scheme is designed. Through the gain scheduling method, the parameters in the extended state observer algorithm and the control law are adjusted in real time. The parameters of the improved active disturbance rejection control algorithm can be adjusted in real time according to the operating conditions of the actual industrial system to achieve satisfactory control effects, thereby providing support for ensuring the control quality of a type of actual industrial system under all operating conditions.

[0006] The present invention proposes an improved active disturbance rejection control implementation method based on gain scheduling, which is characterized by comprising the following steps:

[0007] A high-order inertial system is used to describe a class of real industrial systems;

[0008] The controlled variable of a real industrial system or the output of the transfer function of a high-order inertial system is selected as the scheduling parameter. The full operating condition of the real industrial system is divided into multiple scheduling intervals according to the operating conditions of the scheduling parameters. A gain scheduling scheme is designed based on the scheduling parameters of the scheduling intervals. Based on the gain scheduling scheme, a compensation algorithm for improving the active disturbance rejection control strategy is designed.

[0009] The current control quantity of the actual industrial system is used as the input of the compensation algorithm of the improved active disturbance rejection control strategy to obtain the next calculation step value of the compensation algorithm output; the next calculation step value of the output of the actual industrial system and the next calculation step value of the output of the compensation algorithm are used to design an extended state observer algorithm to obtain tracking values of the next two calculation step values of the output of the actual industrial system, tracking values of the next two calculation step values of the multi-order derivatives of the output of the actual industrial system, and tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system;

[0010] The following two calculation step values under the output of the actual industrial system, the tracking values of the following two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance of the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the following three calculation step values of the actual industrial system input;

[0011] Alternatively, the tracking values of the two calculation step values under the output of the actual industrial system, the tracking values of the next two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the next three calculation step values of the actual industrial system input;

[0012] The obtained next three-step calculation step values of the actual industrial system input are used to update the next two-step calculation step values of the actual industrial system input, adjust the opening of the actuator, and realize the control quantity adjustment of the closed-loop system, thereby realizing the regulation of the output of the controlled object.

[0013] The present invention also provides an improved active disturbance rejection control system based on gain scheduling, comprising: a controlled actual industrial system, an actuator, a compensation calculator for performing compensation algorithm calculations, a control law calculator for performing control law calculations, and an extended state observer for performing extended state observer algorithm calculations; the control law calculator, the compensation calculator, the extended state observer, and the actuator are communicatively connected to the controlled actual industrial system to implement the aforementioned improved active disturbance rejection control implementation method based on gain scheduling.

[0014] The characteristics and beneficial effects of the present invention are:

[0015] The present invention proposes an implementation method of an improved active disturbance rejection control strategy based on gain scheduling. This method retains the existing improved active disturbance rejection control algorithm while taking into account the tracking capability and anti-interference capability of such high-order inertial systems. Through gain scheduling, the improved active disturbance rejection control algorithm is adjusted and optimized in real time, which can ensure that a class of actual industrial systems have satisfactory control effects under strong nonlinearity and a wide range of variable working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a structural diagram of an existing improved active disturbance rejection control algorithm;

[0017] Figure 2 This is the structural block diagram of another existing improved active disturbance rejection control algorithm;

[0018] Figure 3 This is a structural block diagram of an anti-saturation auto-disturbance rejection control algorithm of the present invention;

[0019] Figure 4 The present invention provides an implementation step of an improved active disturbance rejection control method based on gain scheduling;

[0020] Figure 5 A comparison chart of the set values, the output values of the method of the present invention, and the output values of the comparative method in a specific implementation case;

[0021] Figure 6 This is a structural block diagram of another anti-saturation auto-disturbance rejection control algorithm of the present invention;

[0022] Figure 7 These are the implementation steps of another improved active disturbance rejection control method based on gain scheduling of the present invention. DETAILED DESCRIPTION

[0023] The following will describe in detail various exemplary embodiments of the present invention in conjunction with specific embodiments. The description of the exemplary embodiments is merely illustrative and does not limit the present invention and its application or use. The present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to make the present invention thorough and complete and to fully convey the scope of the present invention to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps described in these embodiments should be interpreted as merely exemplary and not as limiting.

[0024] All terms (including technical or scientific terms) used in the present invention have the same meaning as those understood by ordinary technicians in the field to which the present invention belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries should be interpreted as having the meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined herein.

[0025] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0026] The following is further described in detail with reference to the accompanying drawings and specific embodiments.

[0027] Example 1

[0028] This embodiment provides an improved active disturbance rejection control system based on gain scheduling, such as Figure 3 As shown, it includes: a controlled actual industrial system, an actuator, a compensation calculator for performing compensation algorithm calculation, a control law calculator for performing control law calculation, and an extended state observer for performing extended state observer algorithm calculation; the control law calculator, the compensation calculator, the extended state observer, and the actuator are communicatively connected with the controlled actual industrial system to implement an improved active disturbance rejection control method based on gain scheduling.

[0029] The steps of the improved active disturbance rejection control implementation method based on gain scheduling are as follows: a high-order inertial system is used to describe a class of actual industrial systems;

[0030] The controlled variable of a real industrial system or the output of the transfer function of a high-order inertial system is selected as the scheduling parameter. The full operating condition of the real industrial system is divided into multiple scheduling intervals according to the operating conditions of the scheduling parameters. A gain scheduling scheme is designed based on the scheduling parameters of the scheduling intervals. Based on the gain scheduling scheme, a compensation algorithm for improving the active disturbance rejection control strategy is designed.

[0031] The current control quantity of the actual industrial system is used as the input of the compensation algorithm of the improved active disturbance rejection control strategy to obtain the next calculation step value of the compensation algorithm output; the next calculation step value of the output of the actual industrial system and the next calculation step value of the output of the compensation algorithm are used to design the input of the extended state observer algorithm to obtain the tracking values of the next two calculation step values of the output of the actual industrial system, the tracking values of the next two calculation step values of the multi-order derivatives of the output of the actual industrial system, and the tracking values of the two calculation steps under the total disturbance suffered by the actual industrial system;

[0032] The following two calculation step values under the output of the actual industrial system, the tracking values of the following two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance of the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the following three calculation step values of the actual industrial system input;

[0033] The obtained next three-step calculation step values of the actual industrial system input are used to update the next two-step calculation step values of the actual industrial system input, adjust the opening of the actuator, and realize the control quantity adjustment of the closed-loop system, thereby realizing the regulation of the output of the controlled object.

[0034] Specifically, taking the power control system of a circulating fluidized bed as an actual industrial system, the steps of implementing the improved active disturbance rejection control method based on gain scheduling are described in detail, such as Figure 4 As shown:

[0035] Step 1: The power control system of the circulating fluidized bed is described by a transfer function in the form of a series inertia link. The mathematical expression of the transfer function is:

[0036]

[0037] The output Y(s) and input U(s) of the transfer function are represented by y(k) and u(k) in each calculation step, respectively. k represents the calculation step, s, K, T, and n represent the differential operator, the gain of the transfer function, the time constant of the transfer function, and the order of the transfer function, respectively, and n ≥ 3.

[0038] Step 2: Select the scheduling parameter. The output of the transfer function, i.e., power, is selected as the scheduling parameter. The scheduling parameter is defined as ρ.

[0039] Step 3: Divide the scheduling interval. According to the operating conditions of the scheduling parameters, the full working conditions of the actual industrial system are divided into p scheduling intervals. The boundary of each scheduling interval is represented by the subscript q (1≤q≤p, and it is a positive integer). The left boundary of the scheduling parameter in the qth scheduling interval is represented by ρ q , the right boundary of the scheduling parameter of the qth scheduling interval is expressed as ρq+1 And ρ q <ρ q+1 ,The parameters of the improved ADRC strategy and the transfer function of the actual industrial system also adopt the same ,expression method;

[0040] Step 4: Design a compensation algorithm to improve the ADRC strategy. The mathematical expression of the compensation algorithm is:

[0041]

[0042] Among them U c (s) is the output of the compensation algorithm, m is the order of the compensation algorithm, which is a positive integer and m∈[1,n], T c is the time constant of the compensation algorithm, output U c (s) in the next calculation step and input U(s) in the current calculation step respectively with u c (k+1) and u(k), k represents the calculation step sequence; the time constant T of the compensation algorithm c The value of depends on the value of the scheduling parameter ρ, which is calculated as follows:

[0043]

[0044] Where T c_1 and T c_2 is the time constant T c The compensation algorithm is at the left and right boundaries of the first scheduling interval, T c_(q-1) and T c_q is the time constant T c The compensation algorithm is used at the left and right boundaries of the q-1th scheduling interval, T c_p and T c_(p+1) is the time constant T c The compensation algorithm is at the left and right boundaries of the pth scheduling interval;

[0045] Step 5: Use the output of the actual industrial system in step 1 to calculate the next step sequence value y(k+1) and the output of the compensation algorithm obtained in step 4 to calculate the next step sequence value u c (k+1) Design an extended state observer algorithm to obtain the tracking value z1(k+2) of the next two calculation step values of the actual industrial system output y(k+2), the tracking value z2(k+2) of the next two calculation step values of the first-order derivative of the actual industrial system output, ... the tracking value z of the next two calculation step values of the first-order derivative of the actual industrial system output (1≤j≤nm and is a positive integer) j (k+2)…, the tracking value z of the next two calculation steps of the nm-order derivative output of the actual industrial system n-m (k+2) and the tracking value z of the two calculation step sequence values under the total disturbance of the actual industrial systemn-m+1 (k+2);

[0046] z1(k+2), z2(k+2), z j (k+2), z n-m (k+2) and z n-m+1 The (k+2) extended state observer algorithm is:

[0047]

[0048] Where h is the sampling period, and the value range of h is [0.001,100]; l1, l j 、l n-m+1 and b0 are the changing parameters of the improved ADRC strategy, where l1 refers to the first extended state observer gain coefficient, l j Refers to the j-th extended state observer gain coefficient, l n-m+1 Refers to the n-m+1th extended state observer gain coefficient;

[0049] l1 is calculated by the following formula:

[0050]

[0051] where l 1_1 and l 1_2 is the left and right boundary of l1 in the first scheduling interval, l 1_(q-1) and l 1_q is the left and right boundary of l1 in the q-1th scheduling interval, l 1_p and l 1_(p+1) are the left and right boundaries of l1 in the pth scheduling interval;

[0052] l j Calculate using the following formula:

[0053]

[0054] where l j_1 and l j_2 l j At the left and right boundaries of the first scheduling interval, l j_(q-1) and l j_q l j At the left and right boundaries of the q-1th scheduling interval, l j_p and l j_(p+1) l j At the left and right boundaries of the pth scheduling interval;

[0055] l n-m+1 Calculate using the following formula:

[0056]

[0057] where l n-m+1_1 and l n-m+1_2 for l n-m+1 At the left and right boundaries of the first scheduling interval, l n-m+1_(q-1) and l n-m+1_q for l n-m+1 At the left and right boundaries of the q-1th scheduling interval, l n-m+1_p and l n-m+1_(p+1) for l n-m+1 At the left and right boundaries of the pth scheduling interval;

[0058] b0 is calculated by the following formula

[0059]

[0060] where b 0_1 and b 0_2 is the left and right boundary of b0 in the first scheduling interval, b 0_(q-1) and b 0_q are the left and right boundaries of b0 in the q-1th scheduling interval, b 0_p and b 0_(p+1) are the left and right boundaries of b0 in the pth scheduling interval;

[0061] Step 6: The next two calculation step sequence values y(k+2) of the actual industrial system output obtained in step 5, the tracking value z2(k+2) of the next two calculation step sequence values of the first-order derivative of the actual industrial system output, ... the tracking value z of the next two calculation step sequence values of the first-order derivative of the actual industrial system output (2≤s≤nm and is a positive integer) are converted into s (k+2)…, the tracking value z of the next two calculation steps of the nm-order derivative output of the actual industrial system n-m (k+2) and the tracking value z of the two calculation step sequence values under the total disturbance of the actual industrial system n-m+1 (k+2), combined with the two calculation step sequence values r(k+2) under the set value of a type of controlled actual industrial system, the next three calculation step sequence values u(k+3) of the actual industrial system input are obtained through the control law algorithm;

[0062] u(k+3) can be calculated as follows:

[0063]

[0064] where k1, ..., k s ,…,k n-m To improve the change parameter of the active disturbance rejection control strategy, k1 is calculated by the following formula:

[0065]

[0066] where k 1_1 and k 1_2 is the left and right boundary of k1 in the first scheduling interval, k 1_(q-1) and k 1_q are the left and right boundaries of k1 in the q-1th scheduling interval, k 1_p and k 1_(p+1) are the left and right boundaries of k1 in the pth scheduling interval;

[0067] k s Calculate using the following formula:

[0068]

[0069] where k s_1 and k s_2 k s At the left and right boundaries of the first scheduling interval, k s_(q-1) and k s_q k s At the left and right boundaries of the q-1th scheduling interval, k s_p and k s_(p+1) k s At the left and right boundaries of the pth scheduling interval;

[0070] k n-m Calculate using the following formula:

[0071]

[0072] where k n-m_1 and k n-m_2 k n-m At the left and right boundaries of the first scheduling interval, k n-m_(q-1) and k n-m_q k n-m At the left and right boundaries of the q-1th scheduling interval, k n-m_p and k n-m_(p+1) k n-m At the left and right boundaries of the pth scheduling interval;

[0073] In step 7, the value u(k+2) of the next two calculation steps of the actual industrial system input is updated to the value u(k+3) of the next three calculation steps of the actual industrial system input obtained in step 6, and the opening of the actuator is adjusted to adjust the control quantity of the closed-loop system, thereby adjusting the output of the controlled object.

[0074] Example 2

[0075] This embodiment takes the actual industrial system mentioned in the document "Wu Zhenlong, Li Donghai, Xue Yali, et al. Modified active disturbance rejection control for fluidized bed combustor [J]. ISA Transactions, 2020, 102: 135-153." as an example. In this embodiment, n=5, K and T vary with different working conditions. Specifically,

[0076] In this embodiment, the full working condition of the actual industrial system is divided into two scheduling intervals, and the corresponding scheduling parameters are ρ1=24.31, ρ2=26.33, and ρ3=27.81; correspondingly, K1=K2=K3=8.1, T1=100, T2=110, and T3=120;

[0077] In this embodiment, m=4, so the time constant T of the compensation algorithm is obtained c The values are as follows:

[0078]

[0079] In this embodiment, h=0.05, and the extended state observer algorithm for z1(k+2) and z2(k+2) is:

[0080]

[0081] Where l1 = 0.6, l2 = 0.09 and b0 = 0.005, that is, l 1_1 =l 1_2 =l 1_3 =0.6, l 2_1 =l 2_2 =l 2_3 = 0.09 and b 0_1 =b 0_2 =b 0_3 =0.005;

[0082] In this embodiment, u(k+3) can be calculated by the following formula:

[0083]

[0084] Where b0 = 0.005, k1 is calculated by the following formula:

[0085]

[0086] Figure 5The comparison chart of the set value, the output value of the method of the present invention and the output value of the comparative method in this embodiment case; the document "Wu Zhenlong, Li Donghai, Xue Yali, et al. Modified active disturbance rejection control for fluidized bed combustor[J].ISATransactions,2020,102:135-153." Or the parameters of the improved ADRC algorithm in patent CN108287466B are: T=100, n=5, m=3, b0=0.005, l1=0.9, l2=0.27, l3=0.009, k1=0.0025 and k2=0.10; the parameters of the standard ADRC algorithm are: b0=0.005, l1=0.09, l2=0.0027, l3=0.000009, k1=0.0025 and k2=0.10; the parameters of the Skogestad internal model control (SIMC) PI controller ("PI SIMC ”) is the parameter k p = 0.15 and k i =1 / 666.7. The thin solid line, thick solid line, thick dashed line, dotted line and thin dashed line are the set value of the circulating fluidized bed power system, the output value of the method of the present invention, the comparison method (patent CN108287466B), the standard active disturbance rejection control algorithm and the PI SIMC The output value of .

[0087] The specific simulation process is as follows: at the start of the simulation, the system is in a steady-state state, the set value is changed from 0 to 1 at 100s, the set value is changed from 24.31MW to 25.34MW at 1000s, the set value is changed from 25.34MW to 26.33MW at 10000s, the set value is changed from 26.33MW to 27.38MW at 22000s, and the set value is changed from 27.38MW to 27.81MW at 40000s. From the simulation results, it can be seen that both the method of the present invention and the comparative method can take into account the tracking ability and anti-interference ability of the system. When operating under full working conditions, that is, from 24.31MW to 27.81MW, the present invention can ensure the best control effect, with the smallest overshoot zero and the fastest tracking speed in all working conditions.

[0088] Example 3

[0089] This embodiment provides an improved active disturbance rejection control system based on gain scheduling, such as Figure 6As shown, it includes: a controlled actual industrial system, an actuator, a compensation calculator for performing compensation algorithm calculation, a control law calculator for performing control law calculation, and an extended state observer for performing extended state observer algorithm calculation; the control law calculator, the compensation calculator, the extended state observer, and the actuator are communicatively connected with the controlled actual industrial system to implement an improved active disturbance rejection control method based on gain scheduling.

[0090] The steps of the improved active disturbance rejection control implementation method based on gain scheduling are as follows: a high-order inertial system is used to describe a class of actual industrial systems;

[0091] The controlled variable of a real industrial system or the output of the transfer function of a high-order inertial system is selected as the scheduling parameter. The full operating condition of the real industrial system is divided into multiple scheduling intervals according to the operating conditions of the scheduling parameters. A gain scheduling scheme is designed based on the scheduling parameters of the scheduling intervals. Based on the gain scheduling scheme, a compensation algorithm for improving the active disturbance rejection control strategy is designed.

[0092] The current control quantity of the actual industrial system is used as the input of the compensation algorithm of the improved active disturbance rejection control strategy to obtain the next calculation step value of the compensation algorithm output; the next calculation step value of the output of the actual industrial system and the next calculation step value of the output of the compensation algorithm are used to design an extended state observer algorithm to obtain tracking values of the next two calculation step values of the output of the actual industrial system, tracking values of the next two calculation step values of the multi-order derivatives of the output of the actual industrial system, and tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system;

[0093] The tracking values of the two calculation step values under the output of the actual industrial system, the tracking values of the next two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the next three calculation step values of the actual industrial system input;

[0094] The obtained next three-step calculation step values of the actual industrial system input are used to update the next two-step calculation step values of the actual industrial system input, adjust the opening of the actuator, and realize the control quantity adjustment of the closed-loop system, thereby realizing the regulation of the output of the controlled object.

[0095] In the specific execution process, the expression of the control law algorithm in this embodiment is:

[0096]

[0097] Among them, z1(k+2) is the tracking value of the next two calculation step values of the actual industrial system output y(k+2), z s(k+2) is the tracking value of the next two calculation steps of the derivative of the actual industrial system output (2≤s≤nm and is a positive integer)..., z n-m (k+2) is the tracking value z of the next two calculation steps of the actual industrial system output nm order derivative n-m (k+2), z n-m+1 (k+2) is the tracking value of the two calculation step sequence values under the total disturbance of the actual industrial system, and r(k+2) is the two calculation step sequence values under the set value of a type of controlled actual industrial system;

[0098] where k1, ..., k s ,…,k n-m To improve the change parameter of the ADRC strategy, k1 refers to the first control law coefficient, that is, the first change parameter of the control law in the improved ADRC strategy; k s Refers to the sth control law coefficient, that is, the sth change parameter of the control law in the improved active disturbance rejection control strategy; k n-m Refers to the nmth control law coefficient, that is, the nmth variable parameter of the control law in the improved active disturbance rejection control strategy;

[0099] k1 is calculated by the following formula:

[0100]

[0101] where k 1_1 and k 1_2 is the left and right boundary of k1 in the first scheduling interval, k 1_(q-1) and k 1_q are the left and right boundaries of k1 in the q-1th scheduling interval, k 1_p and k 1_(p+1) are the left and right boundaries of k1 in the pth scheduling interval;

[0102] k s Calculate using the following formula:

[0103]

[0104] where k s_1 and k s_2 k s At the left and right boundaries of the first scheduling interval, k s_(q-1) and k s_q k s At the left and right boundaries of the q-1th scheduling interval, k s_p and k s_(p+1) k s At the left and right boundaries of the pth scheduling interval;

[0105] kn-m Calculate using the following formula:

[0106]

[0107] where k n-m_1 and k n-m_2 k n-m At the left and right boundaries of the first scheduling interval, k n-m_(q-1) and k n-m_q k n-m At the left and right boundaries of the q-1th scheduling interval, k n-m_p and k n-m_(p+1) k n-m At the left and right boundaries of the p-th scheduling interval.

[0108] Therefore, in this embodiment, steps 1 to 5 and 7 in embodiment 1 can be directly adopted, and only step 6 is adjusted, as shown in the following example: Figure 7 As shown, the tracking value z1(k+2) corresponding to the next two calculation step sequence values y(k+2) of the actual industrial system output obtained in step 5, the tracking value z2(k+2) corresponding to the next two calculation step sequence values of the first-order derivative of the actual industrial system output, ... the tracking value z of the next two calculation step sequence values of the first-order derivative of the actual industrial system output (2≤s≤nm and is a positive integer) s (k+2)…, the tracking value z of the next two calculation steps of the nm-order derivative output of the actual industrial system n-m (k+2) and the tracking value z of the two calculation step sequence values under the total disturbance of the actual industrial system n-m+1 (k+2), combined with the two calculation step sequence values r(k+2) under the set value of a type of controlled actual industrial system, the next three calculation step sequence values u(k+3) of the actual industrial system input are obtained through the control law algorithm;

[0109]

[0110] This embodiment also takes the actual industrial system mentioned in the document "Wu Zhenlong, Li Donghai, Xue Yali, et al. Modified active disturbance rejection control for fluidized bed combustor [J]. ISA Transactions, 2020, 102: 135-153." as an example. In this embodiment, n=5, K and T change with different working conditions. Specifically,

[0111] In this embodiment, the full working condition of the actual industrial system is divided into two scheduling intervals, and the corresponding scheduling parameters are ρ1=24.31, ρ2=26.33, and ρ3=27.81; correspondingly, K1=K2=K3=8.1, T1=100, T2=110, and T3=120;

[0112] In this embodiment, m=4, so the time constant T of the compensation algorithm is obtained c The values are as follows:

[0113]

[0114] In this embodiment, h=0.05, and the extended state observer algorithm for z1(k+2) and z2(k+2) is:

[0115]

[0116] Where l1 = 0.6, l2 = 0.09 and b0 = 0.005, that is, l 1_1 =l 1_2 =l 1_3 =0.6, l 2_1 =l 2_2 =l 2_3 = 0.09 and b 0_1 =b 0_2 =b 0_3 =0.005;

[0117] In this embodiment, u(k+3) can be calculated by the following formula:

[0118]

[0119] Where b0 = 0.005, k1 is calculated by the following formula:

[0120]

[0121] Example 4

[0122] The difference between this embodiment and embodiment 1 or embodiment 3 is that the controlled variables of the actual industrial system are selected as the scheduling parameters, and the scheduling parameters are also defined as ρ.

[0123] Example 5

[0124] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that when the processor executes the program, the improved auto-disturbance rejection control method based on gain scheduling as described in any one of Embodiments 1-4 is implemented.

[0125] Example 6

[0126] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the improved active disturbance rejection control method based on gain scheduling as described in any one of Embodiments 1-4 is implemented.

[0127] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0128] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0129] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0130] In addition, the functional units in the various embodiments of the present application can be integrated into a processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit. If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

Claims

1. A method for implementing improved active disturbance rejection control based on gain scheduling, characterized in that: The following steps are involved: A high-order inertial system is used to describe a class of real industrial systems; The controlled variable of a real industrial system or the output of the transfer function of a high-order inertial system is selected as the scheduling parameter. The full operating condition of the real industrial system is divided into multiple scheduling intervals according to the operating conditions of the scheduling parameters. A gain scheduling scheme is designed based on the scheduling parameters of the scheduling intervals. Based on the gain scheduling scheme, a compensation algorithm for improving the active disturbance rejection control strategy is designed. The mathematical expression of the compensation algorithm is: Among them U c (s) is the output of the compensation algorithm, m is the order of the compensation algorithm, which is a positive integer and m∈[1,n]; n is the order of the high-order inertial system; T c is the time constant of the compensation algorithm, the time constant T c The value of depends on the value of the scheduling parameter ρ, which is calculated as follows: Where T c_1 and T c_2 is the time constant T c At the left and right boundaries of the first scheduling interval, T c_(q-1) and T c_q is the time constant T c At the left and right boundaries of the q-1th scheduling interval, T c_p and T c_(p+1) is the time constant T c At the left and right boundaries of the pth scheduling interval; The current control quantity of the actual industrial system is used as the input of the compensation algorithm of the improved active disturbance rejection control strategy to obtain the next calculation step value of the compensation algorithm output; the next calculation step value of the output of the actual industrial system and the next calculation step value of the output of the compensation algorithm are used to design an extended state observer algorithm to obtain tracking values of the next two calculation step values of the output of the actual industrial system, tracking values of the next two calculation step values of the multi-order derivatives of the output of the actual industrial system, and tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system; The extended state observer algorithm is: Where k represents the calculation step; z1(k+2) is the tracking value of the next two calculation step values of the actual industrial system output y(k+2); z2(k+2) is the tracking value z2(k+2) of the next two calculation step values of the actual industrial system output first-order derivative, and z j (k+2) is the tracking value of the next two calculation steps of the j-order derivative output of the actual industrial system, z n-m (k+2) is the tracking value of the next two calculation steps of the nm-order derivative output of the actual industrial system, z n-m+1 (k+2) is the tracking value of the two calculation step values under the total disturbance of the actual industrial system; y(k+1) is the output value of the actual industrial system in the next calculation step, u c (k+1) is the value of the compensation algorithm output at the next calculation step; z1(k+1) is the tracking value of the next calculation step value of the actual industrial system output y(k+1), z2(k+1) is the tracking value of the next calculation step value of the actual industrial system output first-order derivative, z j (k+1) is the tracking value of the next calculation step value of the actual industrial system output j-order derivative, z n-m (k+1) is the tracking value of the next calculation step value of the nm-order derivative output by the actual industrial system, z n-m+1 (k+1) is the tracking value of the next calculation step sequence value of the total disturbance suffered by the actual industrial system; where 1≤j≤nm and is a positive integer, h is the sampling period; l1, l j 、l n-m+1 and b0 are the changing parameters of the improved ADRC strategy, where l1 refers to the first extended state observer gain coefficient, l j Refers to the j-th extended state observer gain coefficient, l n-m+1 Refers to the n-m+1th extended state observer gain coefficient; l1 is calculated as follows: where l 1_1 and l 1_2 is the left and right boundary of l1 in the first scheduling interval, l 1_(q-1) and l 1_q is the left and right boundary of l1 in the q-1th scheduling interval, l 1_p and l 1_(p+1) are the left and right boundaries of l1 in the pth scheduling interval; l j Calculate using the following formula: where l j_1 and l j_2 l j At the left and right boundaries of the first scheduling interval, l j_(q-1) and l j_q l j At the left and right boundaries of the q-1th scheduling interval, l j_p and l j_(p+1) l j At the left and right boundaries of the pth scheduling interval; l n-m+1 Calculate using the following formula where l n-m+1_1 and l n-m+1_2 l n-m+1 At the left and right boundaries of the first scheduling interval, l n-m+1_(q-1) and l n-m+1_q l n-m+1 At the left and right boundaries of the q-1th scheduling interval, l n-m+1_p and l n-m+1_(p+1) l n-m+1 At the left and right boundaries of the pth scheduling interval; b0 is calculated by the following formula where b 0_1 and b 0_2 is the left and right boundary of b0 in the first scheduling interval, b 0_(q-1) and b 0_q are the left and right boundaries of b0 in the q-1th scheduling interval, b 0_p and b 0_(p+1) are the left and right boundaries of b0 in the pth scheduling interval; The following two calculation step values under the output of the actual industrial system, the tracking values of the following two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance of the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the following three calculation step values of the actual industrial system input; The expression of the control law algorithm is: The numerical values of the next three calculation steps input by the actual industrial system are represented by u(k+3). Among them, y(k+2) is the numerical value of the next two calculation steps output by the actual industrial system, z s (k+2) is the tracking value of the next two calculation steps of the s-order derivative output of the actual industrial system..., z n-m (k+2) is the tracking value of the next two calculation steps of the nm-order derivative output of the actual industrial system, z n-m+1 (k+2) is the tracking value of the two calculation step values under the total disturbance of the actual industrial system, and r(k+2) is the two calculation step values under the set value of a type of controlled actual industrial system; where 2≤s≤nm and is a positive integer; where k1, ..., k s ,…,k n-m To improve the change parameter of the active disturbance rejection control strategy, k1 is calculated by the following formula: where k 1_1 and k 1_2 is the left and right boundary of k1 in the first scheduling interval, k 1_(q-1) and k 1_q are the left and right boundaries of k1 in the q-1th scheduling interval, k 1_p and k 1_(p+1) are the left and right boundaries of k1 in the pth scheduling interval; k s Calculate using the following formula: where k s_1 and k s_2 k s At the left and right boundaries of the first scheduling interval, k s_(q-1) and k s_q k s At the left and right boundaries of the q-1th scheduling interval, k s_p and k s_(p+1) k s At the left and right boundaries of the pth scheduling interval; k n-m Calculate using the following formula: where k n-m_1 and k n-m_2 k n-m At the left and right boundaries of the first scheduling interval, k n-m_(q-1) and k n-m_q k n-m At the left and right boundaries of the q-1th scheduling interval, k n-m_p and k n-m_(p+1) k n-m At the left and right boundaries of the pth scheduling interval; Alternatively, the tracking values of the two calculation step values under the output of the actual industrial system, the tracking values of the next two calculation step values under the multi-order derivatives of the actual industrial system output, the tracking values of the two calculation step values under the total disturbance suffered by the actual industrial system, and the two calculation step values under the set value of the controlled variable of the actual industrial system are used as inputs of the control law algorithm to obtain the next three calculation step values of the actual industrial system input; The expression of the control law algorithm is: Among them, z1(k+2) is the tracking value of the next two calculation step values of the actual industrial system output y(k+2), z s (k+2) is the tracking value of the next two calculation steps of the s-order derivative output of the actual industrial system..., z n-m (k+2) is the tracking value of the next two calculation steps of the nm-order derivative output of the actual industrial system, z n-m+1 (k+2) is the tracking value of the two calculation step values under the total disturbance of the actual industrial system, and r(k+2) is the two calculation step values under the set value of a type of controlled actual industrial system; where 2≤s≤nm and is a positive integer; where k1, ..., k s ,…,k n-m To improve the change parameter of the ADRC strategy, k1 refers to the first control law coefficient, that is, the first change parameter of the control law in the improved ADRC strategy; k s Refers to the sth control law coefficient, that is, the sth change parameter of the control law in the improved active disturbance rejection control strategy; k n-m Refers to the nmth control law coefficient, that is, the nmth variable parameter of the control law in the improved active disturbance rejection control strategy; k1 is calculated by the following formula: where k 1_1 and k 1_2 is the left and right boundary of k1 in the first scheduling interval, k 1_(q-1) and k 1_q are the left and right boundaries of k1 in the q-1th scheduling interval, k 1_p and k 1_(p+1) are the left and right boundaries of k1 in the pth scheduling interval; k s Calculate using the following formula: where k s_1 and k s_2 k s At the left and right boundaries of the first scheduling interval, k s_(q-1) and k s_q k s At the left and right boundaries of the q-1th scheduling interval, k s_p and k s_(p+1) k s At the left and right boundaries of the pth scheduling interval; k n-m Calculate using the following formula: where k n-m_1 and k n-m_2 k n-m At the left and right boundaries of the first scheduling interval, k n-m_(q-1) and k n-m_q k n-m At the left and right boundaries of the q-1th scheduling interval, k n-m_p and k n-m_(p+1) k n-m At the left and right boundaries of the pth scheduling interval; The obtained next three-step calculation step values of the actual industrial system input are used to update the next two-step calculation step values of the actual industrial system input, adjust the opening of the actuator, and realize the control quantity adjustment of the closed-loop system, thereby realizing the regulation of the output of the controlled object.

2. The method for implementing improved active disturbance rejection control based on gain scheduling according to claim 1, characterized in that: A class of actual industrial systems is described by the transfer function of a high-order system composed of inertia links in series. The mathematical expression of the transfer function is: The output Y(s) and input U(s) of the transfer function are represented by y(k) and u(k) respectively in each calculation step, k represents the calculation step, s, K, T and n represent the differential operator, the gain of the transfer function, the time constant of the transfer function and the order of the transfer function respectively, and n ≥ 3.

3. The method for implementing improved active disturbance rejection control based on gain scheduling according to claim 1, characterized in that: After setting the scheduling parameters, the full working condition of the actual industrial system is divided into p scheduling intervals according to the operating conditions of the scheduling parameters. The boundary of each scheduling interval is represented by the subscript q. The left boundary of the scheduling parameter in the qth scheduling interval is represented by ρ q , the right boundary of the scheduling parameter of the qth scheduling interval is expressed as ρ q+1 And ρ q <ρ q+1 , where 1≤q≤p, and is a positive integer.

4. An improved active disturbance rejection control system based on gain scheduling, characterized in that: include: A controlled actual industrial system, an actuator, a compensation calculator for performing compensation algorithm calculations, a control law calculator for performing control law calculations, and an extended state observer for performing extended state observer algorithm calculations; the control law calculator, the compensation calculator, the extended state observer, and the actuator are communicatively connected to the controlled actual industrial system to implement the improved active disturbance rejection control method based on gain scheduling as described in any one of claims 1 to 3.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the improved active disturbance rejection control method based on gain scheduling according to any one of claims 1 to 3 is implemented.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for implementing the improved active disturbance rejection control based on gain scheduling according to any one of claims 1 to 3 is implemented.

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